It is well known that the Yukawa interaction \(\bar{L}\eta ^cN_R\)  could induce lepton flavor violation process [1]}. Systematic studies on all LFV processes in scotogenic models have already been performed in Ref. [2]}. Currently, MEG experiment has set the most stringent constraint on \(\mu \rightarrow e\gamma \) , which requires BR\((\mu \rightarrow e\gamma )<4.2\times 10^{-13}\)  at 90% CL [3]}. The future upgrade of MEG could push the limit down to about \(6\times 10^{-14}\)  [4]}. Meanwhile, the limits on LFV \(\tau \)  decays are much loose, i.e., BR\((\tau \rightarrow \mu \gamma )<4.4\times 10^{-8}\)  and BR\((\tau \rightarrow e\gamma )<3.3\times 10^{-8}\)  [5]}. Hence, large Yukawa coupling in the \(\tau \)  sector is viable if one imposes hierarchal Yukawa structure as \(|h_{ei}|\lesssim |h_{\mu i}|\lesssim |h_{\tau i}|\)  [6]}. On the other hand, if one consider universal Yukawa structure, then it is clearly expected that the tightest constraint comes from \(\mu \rightarrow e\gamma \) . The corresponding branching ratio is calculated as [2]}
\(\text{BR}(\ell _\alpha \rightarrow \ell _\beta \gamma ) = \frac{3(4\pi ^3)\alpha _\text{em}}{4G_F^2} |A_D|^2 \text{BR}(\ell _\alpha \rightarrow \ell _\beta \nu _\alpha \bar{\nu }_\beta ),\) 
